Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-2x-y &= 4 \\ -6x+y &= 6\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-8x = 10$ Divide both sides by $-8$ and reduce as necessary. $x = -\dfrac{5}{4}$ Substitute $-\dfrac{5}{4}$ for $x$ in the top equation. $-2( -\dfrac{5}{4})-y = 4$ $\dfrac{5}{2}-y = 4$ $-y = \dfrac{3}{2}$ $y = -\dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{5}{4}, \enspace y = -\dfrac{3}{2}$.